The fact that the Constitution was written "without authority" is meaningless because no one has any authority in a government that is just being created. And as litteacher8 points out, it was ratified by the states. The men who created the Constitution were "elitist" in the sense that they were intelligent, educated, and mostly wealthy men. However, who else could have done this job, a rabble of illiterate people? If we view the events of the past week in the Middle East, we can see the consequences of the judgement and actions of a collection of uneducated people without resources.
The Constitution was contemplated as a living document. It is a mere eight pages long, and the framers contemplated that there would not only be amendments, but also that it was a document that would require continuing interpretation. They realized that these eight pages could not possibly cover all eventualities and that times and the country would change. Every time a court relies on the Constitution to make a decision, new life is being breathed into it!